Inclusion Criteria:

          -  Provision of signed and dated, written Informed Consent Form (ICF) prior to any
             trial-specific procedures, sampling, or analyses. If a patient declines to participate
             in the voluntary pharmacogenetics component of the trial, he/she will not be excluded
             from other aspects of the trial.

          -  Patients ≥18 years of age at the time of signature of the ICF

          -  Phase Ia (dose-escalation)

               -  patients with a histologically confirmed diagnosis of advanced, unresectable,
                  and/or metastatic solid tumours (any type).

               -  patients who have received all therapy known to confer clinical benefit
                  (including anti-PD-1 or anti-PDL1 therapies, if relevant), or for whom no therapy
                  of proven efficacy exists, or who are not amenable to standard therapies.
                  Patients with anti- PD-1 or anti-PDL1 experience must have a minimum of 60 days
                  between the last dose of the previous anti PD-1/PD-L1 and Cycle 1 Day 1 of BI
                  754091 treatment.

               -  Patients may agree to provide optional paired biopsies.

          -  Phase Ib (dose expansion)

               -  patients with a histologically confirmed diagnosis of select advanced,
                  unresectable, and/or metastatic solid tumours with either 1) high tumor mutation
                  excluding high microsatellite instability or 2) refractory squamous cell
                  cervical, anal and skin tumors, or 3) recurrent vaginal or vulvar squamous cell
                  carcinoma.

               -  All patients must have measurable lesions according to Response Evaluation
                  Criteria in Solid Tumours (RECIST) v1.1 must have at least 1 tumour lesion
                  amenable to biopsy, and must be medically fit and willing to undergo a biopsy
                  before first treatment and, unless clinically contraindicated, after 6 weeks on
                  therapy

               -  patients who are anti-PD-1 and anti-PDL-1naïve but have failed conventional
                  treatment (excluding anti-PD-1 treatment), or for whom no therapy of proven
                  efficacy exists, or who are not amenable to standard therapies.

          -  Eastern Cooperative Oncology Group (ECOG) score: 0 to 1

          -  Life expectancy of at least 12 weeks after the start of the treatment according to the
             Investigator's judgement

          -  Females of child-bearing potential willing to use adequate contraceptive measures from
             the time of screening until 6 months after trial discontinuation, who are not or will
             not be breast feeding, and agree to have pregnancy tests prior to the start of dosing
             and at regular visits during the trial. Females not of childbearing potential must
             have evidence of such by fulfilling one of the following criteria at screening:

               -  Post-menopausal: defined as more than 50 years-of-age and amenorrhoeic for at
                  least 12 months following cessation of all exogenous hormonal treatments

               -  Documentation of irreversible surgical sterilization by hysterectomy, bilateral
                  oophorectomy, or bilateral salpingectomy

               -  Women under 50 years-of-age would be considered postmenopausal if they have been
                  amenorrhoeic for at least 12 months following the cessation of exogenous hormonal
                  treatments, and have serum follicle-stimulating hormone and luteinizing hormone
                  levels in the postmenopausal range for the institution.

               -  For women of childbearing potential using a contraceptive pill, an additional
                  barrier method is necessary. Acceptable highly effective methods of contraception
                  include total sexual abstinence when this is in line with the preferred and usual
                  lifestyle of the study participant (periodic abstinence such as calendar,
                  ovulation, symptothermal, post-ovulation methods and withdrawal are not
                  acceptable methods of contraception), an intrauterine device or intrauterine
                  hormone-releasing system, bilateral tubal ligation, and vasectomised partner
                  (with post-vasectomy proof of absence of sperm)

          -  Further inclusion criteria apply

        Exclusion criteria:

          -  Major surgery (major according to the Investigator's assessment) performed within 12
             weeks prior to first trial treatment or planned within 12 months after screening,
             e.g.,hip replacement

          -  Patients who must or wish to continue the intake of restricted medications or any drug
             considered likely to interfere with the safe conduct of the trial

          -  Previous enrolment in this trial

          -  Any investigational or anti-tumour treatment within 4 weeks or 5 half-life period
             (whichever is shorter) prior to the initial administration of BI 754091.

          -  Presence of other active invasive cancers other than the one treated in this trial
             within 5 years prior to screening, with the exception of appropriately treated
             basal-cell carcinoma of the skin, in situ carcinoma of the uterine cervix, or other
             local tumours considered cured by local treatment.

          -  Untreated brain metastasis(es) that may be considered active. Patients with previously
             treated brain metastases may participate provided they are stable (i.e., without
             evidence of Progression of Disease by imaging for at least 4 weeks prior to the first
             dose of trial treatment, and any neurologic symptoms have returned to baseline), and
             there is no evidence of new or enlarging brain metastases

          -  Inadequate organ function or bone marrow reserve as demonstrated by the following
             laboratory values:

               -  Absolute neutrophil count <1.5 x 10^9/L (<1500/mm3)

               -  Platelet count <100 x 10^9/L

               -  Haemoglobin <90 g/L (<9 g/dL)

               -  Alanine aminotransferase (ALT) >2.5 times the upper limit of normal (ULN) if no
                  demonstrable liver metastases or >5 times ULN in the presence of liver metastases

               -  Aspartate aminotransferase (AST) >2.5 times ULN if no demonstrable liver
                  metastases or >5 times ULN in the presence of liver metastases

               -  Total bilirubin >1.5 times ULN, except for patients with Gilbert's syndrome who
                  are excluded if total bilirubin >3.0 x ULN or direct bilirubin >1.5 x ULN

               -  Creatinine >1.5 times ULN or creatinine clearance <50 mL/min (measured or
                  calculated by Chronic Kidney Disease Epidemiology (CKD-EPI) Collaboration
                  equation); confirmation of creatinine clearance is only required when creatinine
                  is >1.5 times ULN.

          -  Any of the following cardiac criteria:

               -  Mean resting corrected QT interval (QTc) >470 msec

               -  Any clinically important abnormalities (as assessed by the Investigator) in
                  rhythm, conduction, or morphology of resting Electrocardiograms, e.g., complete
                  left bundle branch block, third degree heart block

               -  Any factors that increase the risk of QTc prolongation or risk of arrhythmic
                  events such as heart failure, hypokalaemia, congenital long QT syndrome, family
                  history of long QT syndrome or unexplained sudden death under 40 years-of-age, or
                  any concomitant medication known to prolong the QT interval

               -  Ejection fraction (EF) <55% or the lower limit of normal of the institutional
                  standard will be excluded. Only in cases where the Investigator (or the treating
                  physician or both) suspects cardiac disease with negative effect on the EF will
                  the EF be measured during screening using an appropriate method according to
                  local standards to confirm eligibility (e.g., echocardiogram [ECHO], multi-gated
                  acquisition scan [MUGA]). A historic measurement of EF no older than 6 months
                  prior to first administration of study drug can be accepted provided that there
                  is clinical evidence that the EF value has not worsened since this measurement in
                  the opinion of the Investigator or of the treating physician or both.

          -  History of pneumonitis within the last 5 years

          -  History of severe hypersensitivity reactions to other monoclonal Antibodies

          -  Immunosuppressive corticosteroid doses (>10 mg prednisone daily or equivalent) within
             4 weeks prior to the first dose of BI 754091

          -  Active autoimmune disease or a documented history of autoimmune disease, except
             vitiligo or resolved childhood asthma/atopy

          -  Known history of human immunodeficiency virus infection or an active hepatitis B or C
             virus infection. HIV infection is allowed for patients in cohort 6 (cervical/anal
             squamous) and cohort 7 (vulvar)

          -  Interstitial lung disease

          -  Chronic alcohol or drug abuse or any condition that, in the Investigator's opinion,
             makes him/her an unreliable trial subject, unlikely to complete the trial, or unable
             to comply with the protocol procedures.